This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. Primary support for the subproject and the subproject's principal investigator may have been provided by other sources, including other NIH sources. The Total Cost listed for the subproject likely represents the estimated amount of Center infrastructure utilized by the subproject, not direct funding provided by the NCRR grant to the subproject or subproject staff. Early stage clinical trials for serious diseases like cancer pose serious challenges in balancing the risks and benefits for the patient enrolled with the costs and benefits to the community, especially the value of the scientific information to be gained. In principle, decision theory provides a clear rational solution to the problem. However, evaluating the value of future knowledge to be gained involves combinatorially explosive calculations. This work adapts and evaluates several approximation methods, including some fairly recent techniques developed for later-stage clinical trials, and also techniques from planning and robotics for solving partially observable Markov decision processes